The Hermitian matrix \(H=I_{n-1} \oplus (-1)\)  defines an indefinite inner product space with one negative square, this is sometimes called the Minkowski space. The formula \([x,y]=\langle Hx,y\rangle \) , with \(x,y\in \mathbb {C}^n\)  and where \(\langle \cdot \, ,\cdot \rangle \)  denotes the standard inner product, defines an indefinite inner product on \(\mathbb {C}^n\) . The function \([x,y]\)  satisfies all the properties of the standard inner product, with the exception that \([x,x]\)  may be nonpositive for \(n\ne 0\) . Basic elements of the theory of indefinite inner product spaces are summarised in [1]}.
